1. We are asked to find the inverse of the function $$f(x) = -1 - \frac{1}{5}x$$ and then graph both the function and its inverse. 2. To find the inverse, start by replacing $$f(x)$$ with $$y$$: $$y = -1 - \frac{1}{5}x$$ 3. Swap $$x$$ and $$y$$ to find the inverse function: $$x = -1 - \frac{1}{5}y$$ 4. Solve for $$y$$: $$x + 1 = -\frac{1}{5}y$$ Multiply both sides by $$-5$$: $$-5(x + 1) = y$$ 5. So the inverse function is: $$f^{-1}(x) = -5(x + 1) = -5x - 5$$ 6. Explanation: The inverse function reverses the effect of the original function. Here, the original function scales $$x$$ by $$-\frac{1}{5}$$ and shifts by $$-1$$. The inverse scales by $$-5$$ and shifts by $$-5$$. 7. For graphing, the original function is a line with slope $$-\frac{1}{5}$$ and y-intercept $$-1$$. 8. The inverse function is also a line with slope $$-5$$ and y-intercept $$-5$$. 9. Both graphs are reflections of each other across the line $$y = x$$. Final answer: $$f^{-1}(x) = -5x - 5$$